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Shaded Square

Age 14 to 16 Short Challenge Level:

The diagram on the right shows a square with side length $2\text{m}$ and lines drawn to its sides from its centre $O$. The points $A$, $B$, $C$ and $D$ are all on different sides of the square.

The lines $OA$ and $OB$ are perpendicular, as are $OC$ and $OD$.

What is the shaded area?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.